Analysis of braid manifolds using uniform manifold approximation and projection

Abstract

Autonomous sonar target recognition has been an ongoing challenge in the underwater signal processing community for many decades. Aspect-dependent target scattering and waveguide propagation causes target features to overlap, which increases the difficulty of constructing feature dictionaries. Current machine learning algorithms can suffer from an inability to track morphing target-specific features. Other ”black-box” machine learning algorithms produce results that are not explainable. We seek to extend previous work on creating feature representations using braid manifolds. Specifically, we use Uniform Manifold Approximation and Projection (UMAP) as a dimensionality reduction technique to search for underlying features that lay on a manifold. UMAP is an unsupervised learning algorithm that is built upon Riemannian geometry and fuzzy simplicial sets. The low dimensional representation embedding that UMAP produces is computed using both stochastic approximate nearest neighbor search and stochastic gradient descent with negative sampling. The performance of UMAP embeddings will be compared against other common dimension reduction algorithms and evaluated using various classifiers. [The authors would like to thank the Office of Naval Research for funding under Grant No. N00014-21-1-2420 and the University of Iowa.]